[d2n-analysis-talk] Background Correction in the PR, GC

[David Flay]

Hi all,

I wanted to mention a few things that I've been wrestling with today
concerning the way in which I subtract my background for these studies.

When making corrections to the GC, it's very straightforward.  I choose an
electron sample in the 2D energy plot of the L.prl1.e vs. L.prl2.e plot. 
Then, I plot that sample in an E/p histogram, subject to two different
cuts -- GC == 0, GC>0.  This tells me which are my 'pions' and which are
my'electrons'.  Therefore, I can fit the pions, and subtract them off
(call this N_pi).  Then, my corrected sample is:

N_cor = N_samp - N_pi.

(N_samp = N_e + pi, where N_e are true electrons; pi = pions)

Thus, a <perfect> subtraction (i.e., N_pi = pi = GetEntries() of the pion
distribution) should give N_e.  Therefore, the corrected efficiency,
eff_c, is ~1.  This is what I can verify from my code.

However, the situation is a bit more tricky when trying to correct a
sample chosen in the <Cerenkov>.  The problem I've noticed is in the cuts
I use to <define> electrons in the PR.

I use: prl_E_P>0.5&&L.prl1.e>200.

If I consider the 'inverse' of that, we have the cut:
prl_E_P<0.5&&L.prl1.e<200 (cut1).  However, I believe this is the
<incorrect> cut to use as choosing 'pions' to plot in the GC, so we may
see how to subtract this off from the chosen sample.

I believe it is more appropriate to use: prl_E_P<0.5||L.prl1.e<200 (cut2).

This is because there are events that satisfy one, but <not> the other,
that may not get subtracted, when they are clearly labeled as
non-electrons when I do my efficiency calculations.  I've attached a
cartoon plot I've drawn to explain this idea. Red = electrons, dark blue =
pions.

Using the form of cut1, the light blue lines are regions that are not
counted as background to be subtracted -- only the half-trapezoid in
magenta is.  If we consider the form of cut2, we now include that light
blue region, and the full boundary of the E/p and PRL1 cut (in green).

If I use cut1, the correction brings me from ~94.9% to 96.8%.  If I use
cut2, the correction gets me up to 99.1%.

While I do think cut2 is the valid cut to use as a <guestimation> of the
background that contaminates my GC electron sample, there are still some
inconsistencies... Since N_cor = N_samp - N_pi, I should get:

N_cor = N_samp - N_pi = N_e + pi - N_pi ~ N_e, in the limit that N_pi is
equal to pi. (Here, that would be when N_pi = GetEntries() of the
histogram of my background events plotted in the GC).  However, I am still
off from this expected result by ~300 events or so.  Either I am doing
something wrong, or maybe it's due to some pions that show up in the PR
but have no corresponding delta electron that may be subtracted off in the
first place?

I may be over thinking this, but it's a sanity check I developed (the
first part, referring to the correction to the GC efficiency -- I was
hoping that it would carry over smoothly to the PR case) to make sure my
subtractions make sense.

Any comments?

Thanks,

Dave

-------------------------------------------------
David Flay
Physics Department
Temple University
Philadelphia, PA 19122

office: Barton Hall, BA319
phone: (215) 204-1331

e-mail: flay at jlab.org
            flay at temple.edu

website: http://www.jlab.org/~flay
              http://quarks.temple.edu
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